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J. Math. Math. Sci.</a> <a href="/?q=in%3A465190" title="Articles in this Issue">2021, Article ID 2104051, 9 p. (2021)</a>. </div> <div class="abstract">Summary: In this study, the mathematical model of the cholera epidemic is formulated and analyzed to show the impact of <span class="zbmathjax-textit">Vibrio cholerae</span> in reserved freshwater. Moreover, the results obtained from applying the new fractional derivative method show that, as the order of the fractional derivative increases, cholera-preventing behaviors also increase. Also, the finding of our study shows that the dynamics of <span class="zbmathjax-textit">Vibrio cholerae</span> can be controlled if continuous treatment is applied in reserved freshwater used for drinking purposes so that the intrinsic growth rate of <span class="zbmathjax-textit">Vibrio cholerae</span> in water is less than the natural death of <span class="zbmathjax-textit">Vibrio cholerae</span>. We have applied the stability theory of differential equations and proved that the disease-free equilibrium is asymptotically stable if \(R_0<1\), and the intrinsic growth rate of the <span class="zbmathjax-textit">Vibrio cholerae</span> bacterium population is less than its natural death rate. The center manifold theory is applied to show the existence of forward bifurcation at the point \(R_0=1\) and the local stability of endemic equilibrium if \(R_0>1\). Furthermore, the performed numerical simulation results show that, as the rank of control measures applied increases from no control, weak control, and strong control measures, the recovered individuals are 55.02, 67.47, and 674.7, respectively. Numerical simulations are plotted using MATLAB software package.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7459469">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A92D30" title="MSC2020">92D30</a> </td> <td class="space"> Epidemiology </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92C60" title="MSC2020">92C60</a> </td> <td class="space"> Medical epidemiology </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Atransmission+dynamics">transmission dynamics</a>; <a href="/?q=ut%3Avibrio+cholerae">vibrio cholerae</a></div> <div class="software"> <h3>Software:</h3><a href="/software/558">Matlab</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1486.92212" data-ciurl="/ci/07459469" data-biburl="/bibtex/07459469.bib" data-amsurl="/amsrefs/07459469.bib" data-xmlurl="/xml/07459469.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07459469.pdf" title="Zbl 1486.92212 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1155/2021/2104051" aria-label="DOI for “Application of a new generalized fractional derivative and rank of control measures on cholera transmission dynamics”" title="10.1155/2021/2104051">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Lin, J.; Xu, R.; Tian, X., Transmission dynamics of cholera with hyperinfectious and hypoinfectious vibrios: mathematical modelling and control strategies, Mathematical Biosciences and Engineering, 16, 5, 4339-4358 (2019) · <a href="/1497.92275" class="nowrap">Zbl 1497.92275</a> · <a href="https://doi.org/10.3934/mbe.2019216" class="nowrap">doi:10.3934/mbe.2019216</a></td> </tr><tr> <td>[2]</td> <td class="space">Lemos-Paião, A. P.; Silva, C. J.; Torres, D. F. M., A cholera mathematical model with vaccination and the biggest outbreak of world’s history, AIMS Mathematics, 3, 4, 448-463 (2018) · <a href="/1429.34054" class="nowrap">Zbl 1429.34054</a> · <a href="https://doi.org/10.3934/Math.2018.4.448" class="nowrap">doi:10.3934/Math.2018.4.448</a></td> </tr><tr> <td>[3]</td> <td class="space">Liao, S., Stability analysis and application of a mathematical cholera model, Mathematical Biosciences and Engineering, 8, 3, 733-752 (2011) · <a href="/1260.92063" class="nowrap">Zbl 1260.92063</a> · <a href="https://doi.org/10.3934/mbe.2011.8.733" class="nowrap">doi:10.3934/mbe.2011.8.733</a></td> </tr><tr> <td>[4]</td> <td class="space">Nyabadza, F.; Aduamah, J. 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O.; Olaniyi, S.; Akinpelu, F. O., Global asymptotic dynamics of a nonlinear illicit drug use system, Journal of Applied Mathematics and Computing, 66, 1-2, 39-60 (2020) · <a href="/1475.92009" class="nowrap">Zbl 1475.92009</a> · <a href="https://doi.org/10.1007/s12190-020-01423-7" class="nowrap">doi:10.1007/s12190-020-01423-7</a></td> </tr><tr> <td>[15]</td> <td class="space">Bakare, E. A.; Hoskova-Mayerova, S., Optimal control analysis of cholera dynamics in the presence of asymptotic transmission, Axioms, 10, 2, 60 (2021) · <a href="https://doi.org/10.3390/axioms10020060" class="nowrap">doi:10.3390/axioms10020060</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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